A Chicken and a Half?!

Date: 05/07/97 at 09:54:56
From: Steve Green
Subject: Word problem Dad asks all the time

If a chicken and a half lays an egg and a half in a day and a half,  
how long does it take to get a dozen eggs? 

Date: 05/13/97 at 10:58:32
From: Doctor Sonya
Subject: Re: Word problem Dad asks all the time

Dear Steve,

This question feels strange to answer, because dealing with half 
chickens and half eggs is not something one normally encounters.  
Because I have no intuitive understanding of half a chicken, I'll  
approach this problem by plugging in simple numbers for the 
complicated numbers (like one and a half).

Let's say we have 1 chicken that lays 1 egg in 1 day. Then how many 
days would it take to get a dozen eggs?  12, right?  Now if we have 2 
chickens that lay 2 eggs in, say, 3 days, how long does it take to get 
a dozen eggs?  Since we are getting 4 eggs every 3 days out of these 
two chickens, it will take 3*3 = 9 days.

So what exactly are we doing when we solve these chicken-egg problems?

Let's see. What I am doing is seeing how many eggs are laid total per 
cycle. In the second situation above, each cycle is three days long. 
Then I find out how many cycles we'll need to go through to get 12 
eggs. If we get 4 eggs per cycle, we'll need 12/4 = 3 cycles. Now I  
multiply the number of cycles by the length of each cycle to get the 
total time it will take. This gives me 3*3 = 9 days. So 2 chickens 
who each lay 2 eggs in three days take 9 days to lay a dozen eggs.  
This method should work no matter what our numbers are.  Try plugging 
in the chicken and a half, the egg and a half, and the day and a half, 
and see what you get.

Write us back if you need more help.

-Doctor Sonya,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/